The sum of two numbers is $29$, and their difference is $9$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 29}$ ${x-y = 9}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 38 $ $ x = \dfrac{38}{2} $ ${x = 19}$ Now that you know ${x = 19}$ , plug it back into $ {x+y = 29}$ to find $y$ ${(19)}{ + y = 29}$ ${y = 10}$ You can also plug ${x = 19}$ into $ {x-y = 9}$ and get the same answer for $y$ ${(19)}{ - y = 9}$ ${y = 10}$ Therefore, the larger number is $19$, and the smaller number is $10$.